Construct four relatively prime integers $a,b,c,d$ such that no three of them are relatively prime.

 

Solve:Let $a,b,c$ share a prime factor $3$.$a,b,d$ share a prime factor 2，$a,c,d$ share a prime factor $5$,$b,c,d$ share a prime factor $7$.Let

\begin{equation}

a=3\times 2\times 5=30

\end{equation}

\begin{equation}

b=3\times 2\times 7=42

\end{equation}

\begin{equation}

c=3\times 5\times 7=105

\end{equation}

\begin{equation}

d=2\times 5\times 7=70

\end{equation}

Done.